A Parliament source said the two-member Ankara trip had been postponed to a later date due to the unspecified "disagreement" with Turkish authorities on the format of the meetings.
Kati Piri, a Dutch Socialist, and German deputy Elmar Brok were due in Turkey on Wednesday and Thursday for a two-day fact finding trip, but this was cancelled at short notice.
Piri told this website the reason she was given for the cancellation was that the Turkish regime "objected" to her presence on the delegation.
"They did not like what I have said about them. It is disappointing, not least as we hoped to meet some opposition MPs," said Piri, who is the standing rapporteur on Turkey.
Parliament President Martin Schulz had arranged the visit following the latest round of arrests of Turkish journalists and opposition politicians in Turkey.
The aim was for the two MEPs to discuss with Turkish Prime Minister Binali Yıldırım how to re-establish the faltering political dialogue between the EU and the Turkish government.
The visit of Turkish EU affairs Minister Ömer Çelik to the European Parliament earlier this week was part of the agreement to keep open political dialogue, said the source.
Brok, who chairs Parliament's foreign affairs committee, and Piri, were supposed to travel to Ankara to hold high-level meetings with Turkish authorities and representatives of the opposition and civil society with a view to restore political dialogue.
Due to differences on the format of the meetings, Schulz, reportedly in agreement with Brok and Piri, decided to postpone the visit "until Parliament's prerogatives are respected."
Schulz issued a statement which read: "The European Parliament is keen to dialogue frankly, openly and in good faith with Turkish authorities.
"For dialogue to happen, a precondition is to accept the autonomy and independence of your interlocutor. Brok and Piri represent the European Parliament and we cannot allow a pick-and-choose approach on who speaks to whom."
He added, "Yesterday, I stated clearly to Minister Çelik the admiration for the democratic vigilance of the Turkish people to safeguard democracy during the attempted coup.
"The objections levied by the EU authorities regard the proportionality of the response of the Turkish government in the wake of the coup. The European Union remains committed to dialogue.
"Dialogue, however, requires the two sides to be willing to talk to each other. I continue to hope that the Parliament will be able to visit Turkey soon."